Search and research of energy-efficient configuration of the power supply network

Model of main structure of power-supply is considered for research of states of working collections of induction motors. Model consists of separate electromechanic modules, which can contain different amount of motors. Modules are connected in different points to main cable, laid from transformer before remoted module. On base of this model is developed software program, intended for finding of optimum parameters of structure of network of power-supply with use the genetic algorithm.


Introduction
To date, many methods, models and algorithms have been developed, aimed at improving the efficiency, reliability and safety of power supply distribution networks, at optimizing power losses of industrial enterprises.In works [1][2][3][4][5] the optimization of the operating modes of the elements of power supply systems is described.This is achieved by a comprehensive account of the parameters and characteristics of the power supply system, rebuilding its structure, voltage regulation and reactive power.
Improving the energy efficiency of the power supply system can be achieved by introducing a frequencycontrolled electric drive.In [6,7] presents the experience of implementation and the problems of using a frequencycontrolled asynchronous electric drive in the mining industry.In particular, the author in the article [8] proposed a method for improving the energy efficiency of multimotor frequency-controlled electric drives of main belt conveyors, based on changing the speed of the conveyor and controlling the magnetic state of the electric motor.Despite the obvious advantages of the frequency-controlled electric drive, there are a number of nuances necessary to take into account when introducing it, as noted in [9].At the same time, additional capital investments are required, which are repaid by the long trouble-free operation of the equipment, and there are electromagnetic drive compatibility problems.A long cable between the frequency converter and the motor leads to cyclically recurring significant overvoltages at the motor terminals, having a devastating effect on the insulation of the electrical machine [10].Leakage currents, including currents through bearings, can cause rapid destruction of bearings and seizure of the rotor.
Based on the above, it can be noted that in many cases neither frequency converters nor soft starters are used.Therefore, in distribution networks with an electromotive load during the direct start-up of powerful motors, the problem of increasing the voltage at the terminals of the motors and reducing energy losses remains open.

Mathematical model of an asynchronous motor in the main power supply network
A structure of electric power supply with an electric load is known for search the energy-efficient configuration of the power supply network [11].Its disadvantage when used in computer modeling is that in order to determine the optimal configurations of the power supply network and to research the operating modes of the set of N asynchronous motors, it is necessary to calculate repeatedly the 2 N electric motors. times, 2 N  ).Therefore, in order to shorten the calculation time, we obtain a model of a power grid of a backbone structure with an electric load powered from a source of limited power, using which N motors are calculated.
A mathematical model of the electrical supply scheme is known, consisting of separate electromechanical modules (Figure 1) [12,13].
In Figure 1 denotes: Nmthe number of electric motors in the module; N -the number of electric motors in the system; Nunumber of the module; jnumber of the electric motor; j M -j-th electric motor; 0 L -length of the common cable; Nu L -cable length of the module Nu ; U - voltage at the beginning of the common cable; u  , u  -the components of the voltage at the beginning of the common cable along the axes α, β; 0 U -voltage at the end of the common cable; In Figure 2 shows the backbone structure of the power supply network, a particular case of which can be considered the structure in Figure 1.In Figure 2 denotes: N_modnumber of modules; ithe serial number of the module.In contrast to the scheme in Figure 1 scheme of power supply in Figure 2 consists of separate electromechanical modules that can contain a different number of motors connected at different points to the trunk cable laid from the transformer to the most remote module.
We introduce the following notation: the index M will refer to the parameters of the trunk cable, and the index K to the parameters of the cables laid from the trunk cable to the modules.
The state of the j-th electric motor is described by a set of differential and algebraic constraints [13][14][15]: with notation according to [13].
It is seen from ( 1) that the state of the j-th electric motor is characterized by the angular velocity of rotation of the rotor and the components of the stator motor voltages.Therefore, consider the algorithm for forming the stator voltage components in the power supply circuit in Figure 2, in order to obtain a mathematical model of an induction motor in the given power supply structure.
Knowing the number of motors Nm(i) in each i-th module, changing the module number i within the specified limits from 1 to N_mod, determine the j motor numbers of the i-th module from the following inequality: Search and research of energy-efficient configuration of the power supply network 3 We introduce some notation in order to simplify the form of the following expressions: , where p corresponds to the module number and varies from 1 to i.
Taking into account the last abbreviations, the required voltage on the stator winding of the j-th motor is determined as follows: Differentiating sj i  and sj i  from (1), we obtain: '' '' 1 ; 1 .
We substitute ( 5) into (4): Combining ( 1) and ( 6), we obtain for the j-th motor: ; We take into account the influence of the transformer on the process of electromechanical energy conversion.
The conjugation conditions for models (7) and (8) according to the Kirchhoff rules: We unite ( 7) and ( 8) taking into account ( 9) and ( 10 Differentiating tr i  , tr i  , in (8), we obtain: Where do we get: Taking into account ( 5) and (10), we write: where j Jthe moment of inertia of the j-th electric motor; network designed to determine the energy-efficient configuration of the power supply network and to research the operating modes of a set of asynchronous motors.

Energy-efficient configuration of the power supply network of the treatment site
Based on the above results, a software tool has been developed to determine the rational (close to optimal) power supply network configurations by various criteria using a genetic algorithm.The program also allows modeling transient processes in asynchronous electric motors operating in nominal modes as part of the power supply network, rational in terms of minimum power losses or minimum cable voltage loss.
A lot of works [16][17][18][19] were devoted to optimization of multi-extremal functions, to solving problems of nonconvex optimization, nonlinear programming, and forecasting using evolutionary-genetic algorithms.When the genetic algorithm is working, the search process ends when you find a solution close to the optimal one, and not an absolutely exact solution.Therefore, such a solution of the problem can be called rational.
Consider the operation of this software for the example of searching for a rational configuration of the power supply network for the treatment site, and also analyze the results.
In Figure 3 shows the scheme of power supply for the treatment site.Electricity supply of the conveyor, the reloader and the crusher is provided from the power train with the transformer BRUSH 1250-6/1,2.In Table shows the parameters of the consumers of the site.
The scheme in Figure 3 corresponds to the layout of the electrical equipment of the treatment site, shown in Figure 4.As a result of the search for a rational configuration of the power supply network in terms of minimum energy losses in the cable network, a scheme is obtained (Figure 5), in which the energy losses are reduced by 17%, and the average value of the voltage practically does not change.

Research of dynamic characteristics of electromechanical system at start-up of electric motors in the power supply system of the treatment site
The operability and adequacy of the mathematical model of the mains supply network with a motor load powered by a limited power source is confirmed by the following computational experiment.In the experiment, the configuration of the power supply network of the treatment site, which was rational for the minimum energy loss in the cable network, was modeled.
As a load on the electric motors of the conveyor, the reloader and the crusher, the torque of resistance was simulated, the value of which was set by the analytical expression: 0, 4 sin(12 ) 0, 4 sin(26 ), где M scalculated torque of resistance on the executive organ; M nomnominal electromagnetic torque motor.In Figures 6, 7, 8 and 9 show the dynamic characteristics of the main indicators of the electromechanical system when starting the electric motors in the power supply system of the treatment site.With the simultaneous start-up of the reloader motors and the crusher from Figure 6 shows that the voltage drop at the motor terminals is approximately 12 %.After the acceleration of the motors, their currents are reduced (Figure 7), and the voltage is restored after 0,5 s to a level lower than the previous value by approximately 20 V, that is, the voltage loss in the network cables and in the transformer.The latter adversely affects the start up electric motors of the conveyor at the time 1 s.When starting the conveyor motors, their currents form voltage drops on the common sections of the main cable with the motors running.There is a decrease in the voltage at the terminals of the motors already running, depending on the length of the common sections of the motor cables, and also due to an additional drop in the resistance of the secondary windings of the transformer.This has an effect on the speed (Figure 8) and the electromagnetic torque (Figure 9) of the crusher motor and the reloader.The torque of the top drive motor of the conveyor is less than that of the lower drive motor, because of the greater distance from the transformer.So for the most remote of the top drive motor of the conveyor, the voltage drop is approximately 30 % of the nominal value.When working under load, this can lead to a prolonged startup and, in the worst case, to "overturn" the electric motor.Then, the voltage is restored after 0,5 s to a level lower than the previous one by about 25 V.At the time of 2 s, the motors are subjected to an alternating load, which leads to voltage fluctuations at the motor terminals and adversely affects their operation.Voltage fluctuations in the network lead to the appearance of electromechanical oscillations on the shafts of the motors (Figure 9).When the crusher and the reloader motors are switched off at a time of 3 s, the voltage on the connected conveyor motors is increased by approximately 25 V.At the time of 4 seconds, the conveyor motors are switched off.From the time 5 s, the above cycle is repeated, since the motors operate in an intermittent S3 mode with a duty cycle of 60 %.
The reliability of the results obtained is confirmed by the fact that the characteristics described above fully correspond to the oscillograms of the starting of an induction motor with power supplied from a limited power source presented in [20][21][22].

Conclusions
1.The mathematical model of an asynchronous motor in the structure of the main power supply network, taking into account the influence of the transformer on the process of electromechanical energy conversion, is obtained.
2. Based on the received model, a software tool was developed to search and research the rational configuration of the power supply network using a genetic algorithm.
3. The efficiency of the software is shown in the example of searching a rational configuration of the power supply network in terms of minimum energy losses in the cable network.
4. The dynamic characteristics of the electromechanical system during the start-up of electric motors in the power supply system of the treatment site are researched.

Figure 1 .
Figure 1.The scheme of power supply, consisting of separate electro-mechanical modules the components of the module voltage along the axes α, β.

Figure 2 .
Figure 2. Backbone structure of the power supply network

cjM
the resistance torque of the j-th motor.As a result, a mathematical model of an asynchronous motor has been obtained as part of a backbone power supply EAI Endorsed on Energy Web 03 2019 -06 2019 | Volume 6 | Issue 23 | e1 Table.Parameters of the consumers of the siteName of the consumerMotor type Un, V Pn, kW Operating

Figure 3 .
Figure 3. Scheme of power supply for the treatment site

Figure 4 .Figure 5 .
Figure 4. Scheme of the location of the electrical equipment of the treatment site

Figure 6 . 7 Figure 7 .Figure 8 .Figure 9 .
Figure 6.Amplitudes of voltages on the windings of stator motors Search and research of energy-efficient configuration of the power supply network EAI Endorsed Transactions on Energy Web 03 2019 -06 2019 | Volume 6 | Issue 23 | e1